Is it bad to leave toothpaste on your face for acne?

Not recommended. Using any toothpaste for your acne can cause more redness and irritation. Please don't ever do this to your face, save the toothpaste for your teeth only.
Yes. Toothpaste will not treat your acne. It can make you face red and painful instead. The chemicals in toothpaste are very irritating to skin. Do or do this. Stick to products made for acne.